How do you evaluate #(- \frac { 2} { 3} ) ^ { 4} \times ( - 3) ^ { 5}#?

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Answer 1 · 2016-12-29T14:19:03

#-48#

#(-2/3)^4 xx (-3)^5#

Let's look at the signs first.

#(-2/3)^4 # has an even index.

There will be four negative signs, which will make a positive.

#(-3)^5# had an odd index

There will be five negative signs, which will make a negative.

Now consider the numbers:

#+(2/3)^4 xx -(3)^5#

#=2^4/3^4 xx -(3^5)" "# use laws of indices to simplify the 3s

#=-2^4xx3^1#

#=-16xx3#

#=-48#